Question

A new study suggests that women with asthma exposed to air pollution, even before conception, significantly increase their risk of delivering a premature baby. The researcher reported gestational ages for two groups of women with asthma – one group of 44 women exposed to air pollution (mean = 34 weeks with a standard deviation of 1 week) and another group of 50 women not exposed to air pollution (mean = 39 weeks with a standard deviation of 1 week). Which one of the following statements is INCORRECT? (Set alpha level at 0.05; Pooled standard deviation = 1)

a. The null hypothesis is that gestational age is not different between women with asthma who are exposed to air pollution and those who are not exposed to air pollution.
b. The ratio of variances is 1.
c. The degrees of freedom is 88.
d. The obtained test statistic is approximately -28.29.
e. The critical test statistic is 1.960.
f. The decision should be to reject the null hypothesis.

Answer 1

The incorrect statement is (d) The obtained test statistic is approximately -28.29 because such a large magnitude for a t-test statistic is unlikely given the provided data and is not plausible for the described hypothesis test.

Step-by-step explanation:

The statement which is INCORRECT in the context of comparing gestational ages between two groups of women with asthma—one exposed to air pollution and the other not exposed—is (d) The obtained test statistic is approximately -28.29. When conducting a hypothesis test for the difference in means between two independent samples, we usually calculate a t-test statistic, which is unlikely to have such an extremely large magnitude given the provided means and standard deviations.

The null hypothesis (a), ratio of variances (b), degrees of freedom (c), and critical test statistic (e) are based on the information provided and standard procedures for hypothesis testing. The decision to reject the null hypothesis (f) would typically be based on whether the obtained test statistic falls within the rejection region determined by the critical value (1.960 for a two-tailed test at alpha level of 0.05).

Answer 2

a

Step-by-step explanation:

Here the NULL hypothesis will be difference in weeks at which baby is delivered is zero between groups of women who were exposed to air pollution and group of women who were not exposed to air pollution